<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this study, the solution of the non-linear influenza disease system (NIDS) is presented using the Morlet wavelet neural networks (MWNNs) together with the optimisation procedures of the hybrid process of global/local search approaches. The genetic algorithm (GA) and sequential quadratic programming (SQP), that is, GA-SQP, are executed as the global and local search techniques. The mathematical form of the NIDS depends upon four groups: susceptible <italic>S</italic>(<italic>y</italic>), infected <italic>I</italic>(<italic>y</italic>), recovered <italic>R</italic>(<italic>y</italic>) and cross-immune individuals <italic>C</italic>(<italic>y</italic>). To solve the NIDS, an error function is designed using NIDS and its leading initial conditions (ICs). This error function is optimised with a combination of MWNNs and GA-SQP to solve for all the groups of NIDS. The comparison of the obtained solutions and Runge–Kutta results is presented to authenticate the correctness of the designed MWNNs along with the GA-SQP for solving NIDS. Moreover, the statistical operators using different measures are presented to check the reliability and constancy of the MWNNs along with the GA-SQP to solve the NIDS.</p>
</abstract>

In this study, the solution of the non-linear influenza disease system (NIDS) is presented using the Morlet wavelet neural networks (MWNNs) together with the optimisation procedures of the hybrid process of global/local search approaches. The genetic algorithm (GA) and sequential quadratic programming (SQP), that is, GA-SQP, are executed as the global and local search techniques. The mathematical form of the NIDS depends upon four groups: susceptible S(y), infected I(y), recovered R(y) and cross-immune individuals C(y). To solve the NIDS, an error function is designed using NIDS and its leading initial conditions (ICs). This error function is optimised with a combination of MWNNs and GA-SQP to solve for all the groups of NIDS. The comparison of the obtained solutions and Runge–Kutta results is presented to authenticate the correctness of the designed MWNNs along with the GA-SQP for solving NIDS. Moreover, the statistical operators using different measures are presented to check the reliability and constancy of the MWNNs along with the GA-SQP to solve the NIDS.

Design of Morlet wavelet neural network to solve the non-linear influenza disease system

National Yunlin University of Science and Technology

Department of Islamic Educational Management

Department of Accounting and Finance, Faculty of Administrative Sciences

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

In this study, the solution of the non-linear influenza disease system (NIDS) is presented using the Morlet wavelet neural networks (MWNNs) together with the...

Design of Morlet wavelet neural network to solve the non-linear influenza disease system

Published Online: Dec 27, 2021

Page range: 2033 - 2048

Received: Jun 17, 2021

Accepted: Sep 24, 2021

DOI: https://doi.org/10.2478/amns.2021.2.00120

Keywords
Non-linear influenza disease system, Morlet wavelet neural networks, sequential quadratic programming, Runge–Kutta, genetic algorithms, numerical measures

© 2023 Zulqurnain Sabir et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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Design of Morlet wavelet neural network to solve the non-linear influenza disease system

Published Online: Dec 27, 2021

Page range: 2033 - 2048

Received: Jun 17, 2021

Accepted: Sep 24, 2021

DOI: https://doi.org/10.2478/amns.2021.2.00120

KeywordsNon-linear influenza disease system, Morlet wavelet neural networks, sequential quadratic programming, Runge–Kutta, genetic algorithms, numerical measures

© 2023 Zulqurnain Sabir et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Keywords
Non-linear influenza disease system, Morlet wavelet neural networks, sequential quadratic programming, Runge–Kutta, genetic algorithms, numerical measures